Polyelectrolyte Brush:SCFT & FTS

Jonghoon LeeGlenn H. Fredrickson

UCSB

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

0 10 20 30 40 50 0

20

40

60

80

100

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0 10 20 30 40 50 0

20

40

60

80

100

0 0.02 0.04 0.06 0.08 0.1 0.12

0 10 20 30 40 50 0

20

40

60

80

100

(a) (b) (c)

Model: Polyelectrolyte solution

: Excluded Volume

: ElectroStatic

: Chain Stretching

Field Theory of PE solution

HS transformation

How to Solve: SCFT & FTS

• SCFT : saddle point (MF) approximation to the FT

• FTS: Full stochastic sampling of the complex field theory with Complex Langevin method

Polyelectrolyte Brush

0 L

PE Brush in SCFT

Neutral Brush in Good solvent:Parabolic (Milner et al., 1988)

CollapsedBrush inPoor solvent

PE Brush in Good solvent: Gaussian (Zhulina et al., 1992)

Neutral Brush: Solvent effect

PE Brush in Poor solvent:1st order transition

• Ross & Pincus, Macromolecules, 1992• Borisov et al., J. Phys. II, 1991• Goeler & Muthukumar, J. Chem. Phys., 1996• Tran et al. Macromolecules, 1999• Gerbert et al. Langmuir

Scaling

MC, Variational

Experiment, 2000

Electrostatic Correlations

• Arrhenius theory of Electrolyte Osmotic Pressure (1887)No interaction between ions in Mean Field→ 1M NaCl = 2M non-electrolytes

• Debye-Hückel theory of Strong Electrolyte (1923): - Strong positional correlations between anions and cations

d

• Like charge attraction (Levin, Rep. Prog. Phys., 2002)• Charge inversion (Grosberg et al., Rev. Mod. Phys., 2002)

Electrostatic Correlation effects on PE Brush

• Collapse & Nonmonotonic behavior of h (f )- Csajka et al., Eur. Phys. J. E., 2001- Santangelo & Lau, Eur. Phys. J. E., 2004

Single tethered PE

PE Brush

PE brush Height:Effect of Correlation

• 3D (8x8x128)• N=24, b=8, Rg0=16, f=0.25• θ solvent

Summary

• Field Theory is formulated for Polyelectrolyte system

• Based on the mean field solution, 1st order collapse transition of PE Brush in poor solvent is predicted

• SCFT & FTS yield qualitatively different results for PE system with strong correlation effects : to be continued…

PE brush Height:Effect of Correlation